Dirichlet kernel

The Dirichlet Dn of order n is defined as


It can be represented as


Proof: It is

k=-nneikt =e-int1-ei(2n+1)t1-eit

The Dirichlet kernel arises in the analysis of periodic functionsMathworldPlanetmath because for any functionMathworldPlanetmath f of period 2π, the convolution of DN and f results in the Fourier-series approximation of order n:

Title Dirichlet kernel
Canonical name DirichletKernel
Date of creation 2013-03-22 14:11:53
Last modified on 2013-03-22 14:11:53
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 10
Author mathwizard (128)
Entry type Definition
Classification msc 26A30
Related topic ExampleOfTelescopingSum